Decidability of One-Clock Weighted Timed Games with Arbitrary Weights

Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTGs have attracted a lot of attention, especially because...

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Vydáno v:Logical methods in computer science Ročník 21, Issue 1
Hlavní autoři: Monmege, Benjamin, Parreaux, Julie, Reynier, Pierre-Alain
Médium: Journal Article
Jazyk:angličtina
Vydáno: Logical Methods in Computer Science Association 01.01.2025
Logical Methods in Computer Science e.V
Témata:
Computation and Language
Computer Science
computer science - computer science and game theory
Computer Science and Game Theory
Formal Languages and Automata Theory
Logic in Computer Science
algorithmic game theory
timed automata
value computation
weighted timed games
ISSN:1860-5974, 1860-5974
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Shrnutí:Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTGs have attracted a lot of attention, especially because they are known to be decidable when only non-negative weights are allowed. However, when arbitrary weights are considered, despite several recent works, their decidability status was still unknown. In this paper, we solve this problem positively and show that the value function can be computed in exponential time (if weights are encoded in unary).
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-21(1:8)2025